Abstract
Lifetime measures of reproductive performance are quantified here by the LRS (Lifetime Reproductive Success), the number of offspring an individual produces over its lifespan. General formulas for the mean, variance and higher moments of LRS are given by van Daalen and Caswell (2017). Yet, the complete set of probabilities for LRS are often essential, since empirical studies have consistently revealed that distributions of lifetime reproductive performance measures are often non-normal, zero-inflated and highly skewed. certainly in the many cases where the distribution is highly skewed or multimodal. We present here a new method for computing the entire probability distribution of LRS for most species described by age+stage models (including age-only and stage-only models). We show below by examples that the distribution of LRS contains new and useful biological insights. The first two illustrative examples are age-only models for two human populations: the Hadza, a Tanzanian group of hunter-foragers, and a North American group called the Hutterites. The next example is a stage-only model for the large evergreen tree Tsuga canadensis. For these three examples, the data were cited and used by van Daalen and Caswell (2017), who kindly provided the matrices used. The last example, is an age+stage model for Roe deer, Capreolus capreolus, based on the data in Plard et al. (2015). In each of the examples we not only produce the full distribution, but we also calculate and discuss the first 3 moments (the same values as the formulas in (van Daalen and Caswell 2017)). Our methods highlight biologically important questions: what factors determine the probability that individuals produce zero offspring during their lifetimes; how skewed the LRS distribution is; what are the effects of skewed LRS distributions on natural selection, effective population size, and life history evolution? We discuss these and other questions, and point towards future work needed in this area.
